Noncommutative Coordinates for Symplectic Representations

Daniele Alessandrini, Stevens Institute of Technology, Hoboken, New Jersey, Olivier Guichard, Universite de Strasbourg et CNRS, France, Eugen Rogozinnikov, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, and Anna Wienhard, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

• 1. Introduction2. Symplectic group, Lagrangians3. Invariants of Lagrangian subspaces4. Moduli spaces of framed and decorated local systems5. Local systems on quivers and their framings6. $\mathcal {X}$-coordinates for maximal representations7. Topology of the space of maximal framed representations8. Singularities of the space of framed maximal representations into $Sp(4,\mathbf {R})$9. General $\mathcal {X}$-coordinates10. $\mathcal {X}$-coordinates for representations into isogenic groups11. $\mathcal {A}$-coordinates for decorated local systemsA. Normal form for pair of quadratic forms